Fully automatic hp adaptive finite element method for the Stokes problem in two dimensions

The paper is devoted to the solution of the Stokes problem using a self-adaptive hp-finite element method (hp-FEM) in two dimensions. The hp-FEM generates a sequence of optimal hp refined meshes delivering exponential convergence rates of the numerical error with respect to the number of degrees of freedom (and CPU time). Optimal meshes are generated by performing a sequence of h and p refinements on an initial mesh provided by the user. The hp-strategy is based on the coarse/fine grid paradigm and the minimization of the projection based interpolation (PBI) error. We employ the Hughes–Franca stabilization method for the stabilization of mixed problem with equal-order elements.